TSTP Solution File: SEU406+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:49:33 EDT 2022
% Result : Theorem 12.15s 3.62s
% Output : Proof 14.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 16:48:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.57 ____ _
% 0.46/0.57 ___ / __ \_____(_)___ ________ __________
% 0.46/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.57
% 0.46/0.57 A Theorem Prover for First-Order Logic
% 0.46/0.57 (ePrincess v.1.0)
% 0.46/0.57
% 0.46/0.57 (c) Philipp Rümmer, 2009-2015
% 0.46/0.57 (c) Peter Backeman, 2014-2015
% 0.46/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.57 Bug reports to peter@backeman.se
% 0.46/0.57
% 0.46/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.57
% 0.46/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.46/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.94 Prover 0: Preprocessing ...
% 1.93/1.12 Prover 0: Warning: ignoring some quantifiers
% 1.93/1.14 Prover 0: Constructing countermodel ...
% 12.15/3.62 Prover 0: proved (2997ms)
% 12.15/3.62
% 12.15/3.62 No countermodel exists, formula is valid
% 12.15/3.62 % SZS status Theorem for theBenchmark
% 12.15/3.62
% 12.15/3.62 Generating proof ... Warning: ignoring some quantifiers
% 13.67/4.00 found it (size 41)
% 13.67/4.00
% 13.67/4.00 % SZS output start Proof for theBenchmark
% 13.67/4.00 Assumed formulas after preprocessing and simplification:
% 13.67/4.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (k4_xboole_0(v2, v3) = v5 & k2_xboole_0(v2, v3) = v4 & v1_xboole_0(v7) & v1_xboole_0(k1_xboole_0) & r2_hidden(v1, v4) & r2_hidden(v0, v4) & ~ v1_xboole_0(v6) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (k4_xboole_0(v11, v10) = v9) | ~ (k4_xboole_0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (k2_xboole_0(v11, v10) = v9) | ~ (k2_xboole_0(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (k4_xboole_0(v9, v8) = v10) | ~ (k2_xboole_0(v8, v10) = v11) | k2_xboole_0(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (k2_xboole_0(v8, v9) = v10) | ~ r2_hidden(v11, v10) | r2_hidden(v11, v9) | r2_hidden(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (k2_xboole_0(v8, v9) = v10) | ~ r2_hidden(v11, v9) | r2_hidden(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (k2_xboole_0(v8, v9) = v10) | ~ r2_hidden(v11, v8) | r2_hidden(v11, v10)) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (k2_xboole_0(v9, v10) = v11) | ? [v12] : (( ~ r2_hidden(v12, v8) | ( ~ r2_hidden(v12, v10) & ~ r2_hidden(v12, v9))) & (r2_hidden(v12, v10) | r2_hidden(v12, v9) | r2_hidden(v12, v8)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (k2_xboole_0(v9, v8) = v10) | ~ v1_xboole_0(v10) | v1_xboole_0(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (k2_xboole_0(v9, v8) = v10) | k2_xboole_0(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (k2_xboole_0(v8, v9) = v10) | ~ v1_xboole_0(v10) | v1_xboole_0(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (k2_xboole_0(v8, v9) = v10) | k2_xboole_0(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (k2_xboole_0(v8, v9) = v10) | ? [v11] : (k4_xboole_0(v9, v8) = v11 & k2_xboole_0(v8, v11) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (k4_xboole_0(v8, k1_xboole_0) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (k2_xboole_0(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (k2_xboole_0(v8, k1_xboole_0) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ v1_xboole_0(v9) | ~ v1_xboole_0(v8)) & ! [v8] : ! [v9] : (v9 = k1_xboole_0 | ~ (k4_xboole_0(k1_xboole_0, v8) = v9)) & ! [v8] : ! [v9] : ( ~ v1_xboole_0(v9) | ~ r2_hidden(v8, v9)) & ! [v8] : ! [v9] : ( ~ m1_subset_1(v8, v9) | v1_xboole_0(v9) | r2_hidden(v8, v9)) & ! [v8] : ! [v9] : ( ~ r2_hidden(v9, v8) | ~ r2_hidden(v8, v9)) & ! [v8] : ! [v9] : ( ~ r2_hidden(v8, v9) | m1_subset_1(v8, v9)) & ! [v8] : (v8 = k1_xboole_0 | ~ v1_xboole_0(v8)) & ? [v8] : ? [v9] : m1_subset_1(v9, v8) & ( ~ r2_hidden(v1, v5) | ~ r2_hidden(v0, v5)) & ( ~ r2_hidden(v1, v5) | ~ r2_hidden(v0, v3)) & ( ~ r2_hidden(v1, v3) | ~ r2_hidden(v0, v5)) & ( ~ r2_hidden(v1, v3) | ~ r2_hidden(v0, v3)))
% 14.04/4.03 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 14.04/4.03 | (1) k4_xboole_0(all_0_5_5, all_0_4_4) = all_0_2_2 & k2_xboole_0(all_0_5_5, all_0_4_4) = all_0_3_3 & v1_xboole_0(all_0_0_0) & v1_xboole_0(k1_xboole_0) & r2_hidden(all_0_6_6, all_0_3_3) & r2_hidden(all_0_7_7, all_0_3_3) & ~ v1_xboole_0(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k4_xboole_0(v3, v2) = v1) | ~ (k4_xboole_0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_xboole_0(v3, v2) = v1) | ~ (k2_xboole_0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k4_xboole_0(v1, v0) = v2) | ~ (k2_xboole_0(v0, v2) = v3) | k2_xboole_0(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v2) | r2_hidden(v3, v1) | r2_hidden(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v1) | r2_hidden(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v0) | r2_hidden(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k2_xboole_0(v1, v2) = v3) | ? [v4] : (( ~ r2_hidden(v4, v0) | ( ~ r2_hidden(v4, v2) & ~ r2_hidden(v4, v1))) & (r2_hidden(v4, v2) | r2_hidden(v4, v1) | r2_hidden(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v1, v0) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v1, v0) = v2) | k2_xboole_0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v0, v1) = v2) | k2_xboole_0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v0, v1) = v2) | ? [v3] : (k4_xboole_0(v1, v0) = v3 & k2_xboole_0(v0, v3) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (k4_xboole_0(v0, k1_xboole_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (k2_xboole_0(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (k2_xboole_0(v0, k1_xboole_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0)) & ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k4_xboole_0(k1_xboole_0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1)) & ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1)) & ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0)) & ? [v0] : ? [v1] : m1_subset_1(v1, v0) & ( ~ r2_hidden(all_0_6_6, all_0_2_2) | ~ r2_hidden(all_0_7_7, all_0_2_2)) & ( ~ r2_hidden(all_0_6_6, all_0_2_2) | ~ r2_hidden(all_0_7_7, all_0_4_4)) & ( ~ r2_hidden(all_0_6_6, all_0_4_4) | ~ r2_hidden(all_0_7_7, all_0_2_2)) & ( ~ r2_hidden(all_0_6_6, all_0_4_4) | ~ r2_hidden(all_0_7_7, all_0_4_4))
% 14.04/4.04 |
% 14.04/4.04 | Applying alpha-rule on (1) yields:
% 14.04/4.04 | (2) k4_xboole_0(all_0_5_5, all_0_4_4) = all_0_2_2
% 14.04/4.04 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (k4_xboole_0(v0, k1_xboole_0) = v1))
% 14.04/4.04 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v0))
% 14.04/4.04 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v2) | r2_hidden(v3, v1) | r2_hidden(v3, v0))
% 14.04/4.05 | (6) ! [v0] : ! [v1] : ( ~ r2_hidden(v1, v0) | ~ r2_hidden(v0, v1))
% 14.04/4.05 | (7) ! [v0] : ! [v1] : (v1 = k1_xboole_0 | ~ (k4_xboole_0(k1_xboole_0, v0) = v1))
% 14.04/4.05 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v0) | r2_hidden(v3, v2))
% 14.04/4.05 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k2_xboole_0(v3, v2) = v1) | ~ (k2_xboole_0(v3, v2) = v0))
% 14.04/4.05 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v0, v1) = v2) | ? [v3] : (k4_xboole_0(v1, v0) = v3 & k2_xboole_0(v0, v3) = v2))
% 14.04/4.05 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v1, v0) = v2) | ~ v1_xboole_0(v2) | v1_xboole_0(v0))
% 14.04/4.05 | (12) r2_hidden(all_0_7_7, all_0_3_3)
% 14.04/4.05 | (13) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (k2_xboole_0(v1, v2) = v3) | ? [v4] : (( ~ r2_hidden(v4, v0) | ( ~ r2_hidden(v4, v2) & ~ r2_hidden(v4, v1))) & (r2_hidden(v4, v2) | r2_hidden(v4, v1) | r2_hidden(v4, v0))))
% 14.04/4.05 | (14) ! [v0] : ! [v1] : ( ~ m1_subset_1(v0, v1) | v1_xboole_0(v1) | r2_hidden(v0, v1))
% 14.04/4.05 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (k2_xboole_0(v0, k1_xboole_0) = v1))
% 14.04/4.05 | (16) ~ v1_xboole_0(all_0_1_1)
% 14.04/4.05 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ v1_xboole_0(v1) | ~ v1_xboole_0(v0))
% 14.04/4.05 | (18) ~ r2_hidden(all_0_6_6, all_0_2_2) | ~ r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.05 | (19) ! [v0] : ! [v1] : ( ~ v1_xboole_0(v1) | ~ r2_hidden(v0, v1))
% 14.04/4.05 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k4_xboole_0(v1, v0) = v2) | ~ (k2_xboole_0(v0, v2) = v3) | k2_xboole_0(v0, v1) = v3)
% 14.04/4.05 | (21) v1_xboole_0(all_0_0_0)
% 14.04/4.05 | (22) ! [v0] : (v0 = k1_xboole_0 | ~ v1_xboole_0(v0))
% 14.04/4.05 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (k2_xboole_0(v0, v1) = v2) | ~ r2_hidden(v3, v1) | r2_hidden(v3, v2))
% 14.04/4.05 | (24) ~ r2_hidden(all_0_6_6, all_0_4_4) | ~ r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.05 | (25) v1_xboole_0(k1_xboole_0)
% 14.04/4.05 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v0, v1) = v2) | k2_xboole_0(v1, v0) = v2)
% 14.04/4.05 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (k2_xboole_0(v1, v0) = v2) | k2_xboole_0(v0, v1) = v2)
% 14.04/4.05 | (28) ~ r2_hidden(all_0_6_6, all_0_2_2) | ~ r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.05 | (29) ? [v0] : ? [v1] : m1_subset_1(v1, v0)
% 14.04/4.05 | (30) ! [v0] : ! [v1] : ( ~ r2_hidden(v0, v1) | m1_subset_1(v0, v1))
% 14.04/4.05 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (k4_xboole_0(v3, v2) = v1) | ~ (k4_xboole_0(v3, v2) = v0))
% 14.04/4.05 | (32) r2_hidden(all_0_6_6, all_0_3_3)
% 14.04/4.05 | (33) k2_xboole_0(all_0_5_5, all_0_4_4) = all_0_3_3
% 14.04/4.05 | (34) ~ r2_hidden(all_0_6_6, all_0_4_4) | ~ r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.05 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (k2_xboole_0(v0, v0) = v1))
% 14.04/4.05 |
% 14.04/4.05 | Instantiating formula (27) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms k2_xboole_0(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 14.04/4.05 | (36) k2_xboole_0(all_0_4_4, all_0_5_5) = all_0_3_3
% 14.04/4.05 |
% 14.04/4.05 | Instantiating formula (5) with all_0_7_7, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms k2_xboole_0(all_0_4_4, all_0_5_5) = all_0_3_3, r2_hidden(all_0_7_7, all_0_3_3), yields:
% 14.04/4.05 | (37) r2_hidden(all_0_7_7, all_0_4_4) | r2_hidden(all_0_7_7, all_0_5_5)
% 14.04/4.05 |
% 14.04/4.05 | Instantiating formula (10) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms k2_xboole_0(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 14.04/4.05 | (38) ? [v0] : (k4_xboole_0(all_0_5_5, all_0_4_4) = v0 & k2_xboole_0(all_0_4_4, v0) = all_0_3_3)
% 14.04/4.05 |
% 14.04/4.05 | Instantiating (38) with all_27_0_13 yields:
% 14.04/4.05 | (39) k4_xboole_0(all_0_5_5, all_0_4_4) = all_27_0_13 & k2_xboole_0(all_0_4_4, all_27_0_13) = all_0_3_3
% 14.04/4.05 |
% 14.04/4.05 | Applying alpha-rule on (39) yields:
% 14.04/4.05 | (40) k4_xboole_0(all_0_5_5, all_0_4_4) = all_27_0_13
% 14.04/4.05 | (41) k2_xboole_0(all_0_4_4, all_27_0_13) = all_0_3_3
% 14.04/4.05 |
% 14.04/4.06 | Instantiating formula (31) with all_0_5_5, all_0_4_4, all_27_0_13, all_0_2_2 and discharging atoms k4_xboole_0(all_0_5_5, all_0_4_4) = all_27_0_13, k4_xboole_0(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 14.04/4.06 | (42) all_27_0_13 = all_0_2_2
% 14.04/4.06 |
% 14.04/4.06 | From (42) and (41) follows:
% 14.04/4.06 | (43) k2_xboole_0(all_0_4_4, all_0_2_2) = all_0_3_3
% 14.04/4.06 |
% 14.04/4.06 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_2_2 and discharging atoms k2_xboole_0(all_0_4_4, all_0_2_2) = all_0_3_3, yields:
% 14.04/4.06 | (44) k2_xboole_0(all_0_2_2, all_0_4_4) = all_0_3_3
% 14.04/4.06 |
% 14.04/4.06 | Instantiating formula (5) with all_0_6_6, all_0_3_3, all_0_4_4, all_0_2_2 and discharging atoms k2_xboole_0(all_0_2_2, all_0_4_4) = all_0_3_3, r2_hidden(all_0_6_6, all_0_3_3), yields:
% 14.04/4.06 | (45) r2_hidden(all_0_6_6, all_0_2_2) | r2_hidden(all_0_6_6, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Instantiating formula (5) with all_0_7_7, all_0_3_3, all_0_4_4, all_0_2_2 and discharging atoms k2_xboole_0(all_0_2_2, all_0_4_4) = all_0_3_3, r2_hidden(all_0_7_7, all_0_3_3), yields:
% 14.04/4.06 | (46) r2_hidden(all_0_7_7, all_0_2_2) | r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (18), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (47) ~ r2_hidden(all_0_6_6, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (45), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (48) r2_hidden(all_0_6_6, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 | Using (48) and (47) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (47) ~ r2_hidden(all_0_6_6, all_0_2_2)
% 14.04/4.06 | (51) r2_hidden(all_0_6_6, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (24), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (52) ~ r2_hidden(all_0_6_6, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Using (51) and (52) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (51) r2_hidden(all_0_6_6, all_0_4_4)
% 14.04/4.06 | (55) ~ r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (34), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (52) ~ r2_hidden(all_0_6_6, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Using (51) and (52) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (51) r2_hidden(all_0_6_6, all_0_4_4)
% 14.04/4.06 | (59) ~ r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (37), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (60) r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Using (60) and (59) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (59) ~ r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 | (63) r2_hidden(all_0_7_7, all_0_5_5)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (46), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (64) r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 | Using (64) and (55) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (55) ~ r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.06 | (60) r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Using (60) and (59) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (48) r2_hidden(all_0_6_6, all_0_2_2)
% 14.04/4.06 | (55) ~ r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (28), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (47) ~ r2_hidden(all_0_6_6, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 | Using (48) and (47) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (48) r2_hidden(all_0_6_6, all_0_2_2)
% 14.04/4.06 | (59) ~ r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (37), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (60) r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Using (60) and (59) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (59) ~ r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 | (63) r2_hidden(all_0_7_7, all_0_5_5)
% 14.04/4.06 |
% 14.04/4.06 +-Applying beta-rule and splitting (46), into two cases.
% 14.04/4.06 |-Branch one:
% 14.04/4.06 | (64) r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.06 |
% 14.04/4.06 | Using (64) and (55) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 |-Branch two:
% 14.04/4.06 | (55) ~ r2_hidden(all_0_7_7, all_0_2_2)
% 14.04/4.06 | (60) r2_hidden(all_0_7_7, all_0_4_4)
% 14.04/4.06 |
% 14.04/4.06 | Using (60) and (59) yields:
% 14.04/4.06 | (49) $false
% 14.04/4.06 |
% 14.04/4.06 |-The branch is then unsatisfiable
% 14.04/4.06 % SZS output end Proof for theBenchmark
% 14.04/4.06
% 14.04/4.06 3483ms
%------------------------------------------------------------------------------